Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D89 |
| unambiguous semidirect product | C89⋊(C2×C3×C72) |
| Fitting, socle, Hall | C3×C72×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C3×C72 |
| Hall | C72×C89 ⋊ C2×C3 |
| Hall | C3×C89 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D89 |
| commutator, cosocle, hypocenter | C89 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C89 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3×C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13083 |
6762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 36);